Abstract

The statistical literature on assessing the accuracy of risk factors or disease markers as diagnostic tests deals almost exclusively with settings where the test, Y, is measured concurrently with disease status D. In practice, however, disease status may vary over time and there is often a time lag between when the marker is measured and the occurrence of disease. One example concerns the Framingham Risk Score as a marker for the future risk of cardiovascular events, events that occur after the score is ascertained. To evaluate such a marker, one needs to take the time lag into account since the accuracy may be higher when the marker is measured closer to the time of disease occurrence. We therefore consider inference for sensitivity and specificity functions that are defined as functions of time. Semi-parametric regression models are proposed. Data from a cohort study are used to estimate model parameters. One issue that arises in practice is that event times may be censored. In this research, we extend the work by Leisenring, Pepe and Longton (1997) that dealt only with binary tests, parametric models to continuous tests, semi-parametric models and censored data. Asymptotic distribution theory for parameter estimates is produced and procedures for making statistical inference are evaluated with simulation studies. We illustrate our methods with a dataset from the Cardiovascular Health Study, relating the Framingham risk score measured at enrollment to subsequent risk of cardiovascular events.